bSpline {splines2}R Documentation

B-Spline Basis for Polynomial Splines

Description

Generates the B-spline basis matrix representing the family of piecewise polynomials with the specified interior knots and degree, evaluated at the values of x.

Usage

bSpline(
  x,
  df = NULL,
  knots = NULL,
  degree = 3L,
  intercept = FALSE,
  Boundary.knots = NULL,
  ...
)

Arguments

x

The predictor variable. Missing values are allowed and will be returned as they are.

df

Degree of freedom that equals to the column number of returned matrix. One can specify df rather than knots, then the function chooses df - degree - as.integer(intercept) internal knots at suitable quantiles of x ignoring missing values and those x outside of the boundary. If internal knots are specified via knots, the specified df will be ignored.

knots

The internal breakpoints that define the spline. The default is NULL, which results in a basis for ordinary polynomial regression. Typical values are the mean or median for one knot, quantiles for more knots.

degree

A non-negative integer specifying the degree of the piecewise polynomial. The default value is 3 for cubic splines. Zero degree is allowed for piece-wise constant bases.

intercept

If TRUE, the complete basis matrix will be returned. Otherwise, the first basis will be excluded from the output.

Boundary.knots

Boundary points at which to anchor the spline basis. By default, they are the range of the non-NA data. If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.knots.

...

Optional arguments that are not used.

Details

This function extends the bs() function in splines package for B-spline basis by allowing piecewise constant (left-closed and right-open except on the right boundary) spline basis with zero degree.

Value

A numeric matrix with length(x) rows and df columns if df is specified or length(knots) + degree + as.integer(intercept) columns if knots are specified instead. Attributes that correspond to the arguments specified are returned for usage of other functions in this package.

See Also

dbs for derivatives of B-splines; ibs for integrals of B-splines;

Examples

library(splines2)

x <- seq.int(0, 1, 0.01)
knots <- c(0.3, 0.5, 0.6)

## cubic B-splines
bsMat <- bSpline(x, knots = knots, degree = 3, intercept = TRUE)

par(mar = c(2.5, 2.5, 0.2, 0.1), mgp = c(1.5, 0.5, 0))
matplot(x, bsMat, type = "l", ylab = "Cubic B-spline Bases")
abline(v = knots, lty = 2, col = "gray")

## the first derivaitves
d1Mat <- deriv(bsMat)

## the second derivaitves
d2Mat <- deriv(bsMat, 2)

## evaluate at new values
predict(bsMat, c(0.125, 0.801))
[Package splines2 version 0.3.1 Index]